Young Americans between the ages of 20 and 34 drive on avera

Young Americans between the ages of 20 and 34 drive on average 15,098 miles per year, with a standard deviation of 6,000 miles.

Suppose the distribution of miles driven is approxiately normal. What porportion of young americans drive less than 10,000 miles per year.

Please show how to get the answer!!

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    10000      
u = mean =    15098      
          
s = standard deviation =    6000      
          
Thus,          
          
z = (x - u) / s =    -0.849666667      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.849666667   ) =    0.197755218 [ANSWER]